d.If the managers of the two companies collude, what are the equilibrium values of QE, QD, and P? What are each firm’s profits?If the firms split the market equally, total cost in the industry is 1022QQTT+; therefore, MCQT=+10. Total revenue is 100QT-QT2; therefore, MR=100-2QT.To determine the profit-maximizing quantity, set MR = MC and solve for QT:100-2QT=10+QT, or QT=30.This means QE = QD = 15.Substituting QT into the demand equation to determine price:P = 100 - 30 = $70.The profit for each firm is equal to total revenue minus total cost:πi=70(2915(29-10(2915(29+1522=$787.50 million.10. Two firms produce luxury sheepskin auto seat covers, Western Where (WW) and B.B.B. Sheep (BBBS). Each firm has a cost function given by:C (q) = 30q + 1.5q2The market demand for these seat covers is represented by the inverse demand equation:P = 300 - 3Q,where Q = q1 + q2 , total output.a.If each firm acts to maximize its profits, taking its rival’s output as given (i.e., the firms behave as Cournot oligopolists), what will be the equilibrium quantities selected by each firm? What is total output, and what is the market price? What are the profits for each firm?We are given each firm’s cost function C(q) = 30q + 1.5q2 and the market demand function P = 300 - 3Q where total output Q is the sum of each firm’s output q1 and q2. We find the best response functions for both firms by setting marginal revenue equal to marginal cost (alternatively you can set up the profit function for each firm and differentiate with respect to the quantity produced for that firm):R1 = P q1 = (300 - 3(q1 + q2)) q1 = 300q1 - 3q12 - 3q1q2.MR1 = 300 - 6q1 - 3q2MC1 = 30 + 3q1300 - 6q1 - 3q2 = 30 + 3q1210

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Chapter 12: Monopolistic Competition and Oligopolyq1 = 30 - (1/3)q2.By symmetry, BBBS’s best response function will be:q2 = 30 - (1/3)q1.Cournot equilibrium occurs at the intersection of these two best response functions, given by:q1 = q2 = 22.5.Thus,Q = q1 + q2 = 45P = 300 - 3(45) = $165.Profit for both firms will be equal and given by:R - C = (165) (22.5) - (30(22.5) + 1.5(22.52)) = $2278.13.b.It occurs to the managers of WW and BBBS that they could do a lot better by colluding. If the two firms collude, what would be the profit-maximizing choice of output? The industry price? The output and the profit for each firm in this case?

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